Related papers: Hypergroup structures of open quantum random walks…
Hypergraph has been selected as a powerful candidate for characterizing higher-order networks and has received increasing attention in recent years. In this article, we study random walks with resetting on hypergraph by utilizing spectral…
Discrete-time quantum walks are considered a counterpart of random walks and the study for them has been getting attention since around 2000. In this paper, we focus on a quantum walk which generates a probability distribution splitting to…
In large-scale quantum networks, quantum repeaters provide an efficient method to distribute entangled states among selected nodes for realizing long-distance and complicated quantum communications. However, extending quantum repeater…
The discrete quantum walk in N dimensions is analyzed from the perspective of its dispersion relations. This allows understanding known properties, as well as designing new ones when spatially extended initial conditions are considered.…
In this paper we study discrete-time quantum walks on Cayley graphs corresponding to Dihedral groups, which are graphs with both directed and undirected edges. We consider the walks with coins that are one-parameter continuous deformation…
We show that the discrete time quantum walk on the Boolean hypercube of dimension $n$ has a strong dispersion property: if the walk is started in one vertex, then the probability of the walker being at any particular vertex after $O(n)$…
Propagation in quantum walks is revisited by showing that very general 1D discrete-time quantum walks with time- and space-dependent coefficients can be described, at the continuous limit, by Dirac fermions coupled to electromagnetic…
We establish the discrete approximation to Brownian motion with varying dimension (BMVD in abbreviation) by random walks. The setting is very similar to that in [11], but here we use a different method allowing us to get rid the…
In this paper, we consider random walks on the isometry groups of general metric spaces. Under some mild conditions, we show that if two non-elementary random walks on a discrete subgroup of the isometry group have non-singular stationary…
The finite dihedral group generated by one rotation and one flip is the simplest case of the non-abelian group. Cayley graphs are diagrammatic counterparts of groups. In this paper, much attention is given to the Cayley graph of the…
We prove that a quantum walk can detect the presence of a marked element in a graph in $O(\sqrt{WR})$ steps for any initial probability distribution on vertices. Here, $W$ is the total weight of the graph, and $R$ is the effective…
We introduce a method to exactly generate bridge trajectories for discrete-time random walks, with arbitrary jump distributions, that are constrained to initially start at the origin and return to the origin after a fixed time. The method…
Several interesting approaches have been reported in the literature on complex networks, random walks, and hierarchy of graphs. While many of these works perform random walks on stable, fixed networks, in the present work we address the…
Quantum walk serves as a versatile tool for universal quantum computing and algorithmic research. However, the implementation of discrete-time quantum walks (DTQWs) with superconducting circuits is still constrained by some limitations such…
We formalize the treatment of directed (or chiral) quantum walks using Hermitian adjacency matrices, bridging two developing fields of research in quantum information and spectral graph theory. We display results and simulations which…
Non-hermitian quantum graphs possessing real (i.e., in principle, observable) spectra are studied via their discretization. The discretized Hamiltonians are assigned, constructively, an elementary pseudometric and/or a more complicated…
We elaborate on a model of quantum random walk proposed by Hillery et. al., and Jeong et. al., which uses the multiports for quantum "coin tossing". The dynamics of this model is analyzed for the case when the multiports are arranged on the…
This article proposes the first discrete-time implementation of Rydberg quantum walk in multi-dimensional spatial space that could ideally simulate different classes of topological insulators. Using distance-selective exchange-interaction…
This paper aims to explore the inherent connection among Heisenberg groups, quantum Fourier transform and (quasiprobability) distribution functions. Distribution functions for continuous and finite quantum systems are examined first as a…
Quantum random walks have been shown to be powerful quantum algorithms for certain tasks on graphs like database searching, quantum simulations etc. In this work we focus on its applications for the graph isomorphism problem. In particular…